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Purpose: The purpose of this paper is to elaborate new calculation schemes for evaluating the strength parameters of railway rolling stock parts with non-local properties of surface layers in the presence of elliptical stress concentrators. Design/methodology/approach: Using the proposed approaches of developed mathematical modelling and open software for calculating FEniCS, it were established the most dangerous angles of stress concentrator orientation and the required thickness of the hardened zones of parts, which ensures their minimum softening during operation. Findings: It is shown that for an elliptical stress concentrator with any orientation angle, there is a certain key size of surface hardening thickness, the exceeding the value of which does not have influence on the operational strength of the parts, but rise the price of technological operations. Research limitations/implications: In this paper proposes a method for computation the impact of the orientation of the surface elliptical stress concentrators on the contact strength of parts under conditions of dominate friction power loads. Practical implications: The obtained results were used to set the modes of plasma hardening, which increase the contact strength of railway parts with elliptical stress concentrators. Originality/value: Using the approaches of contact mechanics, mathematical and computer modelling, methods of controlling the contact strength of the parts with the surface elliptical stress concentrators were proposed for the first time.